Jacobe supta

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These are replies submitted by escorpsy


well i obtained the variation of the action i attached with respect to g_[~mu,~nu] but want to know that it is correct or not.

N[mu](x[~nu]) is unit time like four velocity and phi is brans-dicke scalar field and acction is written with Lorentzian signature(-,+,+,+)and omega is dicke



thank you for your time.


best regards

@Torre in general i mean can we obtain the field equation of an action by variation ? e.g. f(R) gravity.

@ecterrab for (3) i obtained different solution . what is my problem ?



@ecterrab thank you for your comprehensive help. i appricione of the my problem now is how to define f(R) which R is function of a(t) that contravariant derivative or covariant derivative consider its dependence to t . eg. its easy to compute 00 and 11 components of the field equations that i attached handy. T_00 = rho_m+rho_r and T_11=0. and F is derivative of f with respect to R. but how can i define them so that 00 and 11 components of field equations obtain as the pic i attached.

guys with which command and how to calculate for example μ=0 and ν=0 for R_μρνσ+R_ρν g_σμ-R_ρσ g_νμ-R_μν g_σρ+R_μσ g_νρ +R[g_μν g_σρ -g_μσ g_νρ] Covariantderivative^ρ Covariantderivative^σ  f.  where f is a function of R. for a (-dt+dx+dy+dz) metric

thx again and again



@ecterrab for R^ab R_ab , is Ricci[alpha,beta].Ricci[alpha,beta] correct ?

@ecterrab i uptodated my maple to 18 and its works. thx so much , its illustrative. what about R^ab R_ab ?

@ecterrab  thank you very much , but the first line gave the error, (in physics:-setup) wrong left-hand-side in metric = dtheta^2+sin(theta)^2 dphi^2, quite):

@Torre  what about R^ab R_ab ? . acutually i didnt understand the role of 1 in (g,R,[1]) and i dont know how to calculate other components of ricci or rieman tensor. if you can explain and apply the method of using of these commands with a simple metric ,i really appreciate. 

@Torre  thank you for your help. how to find riemann tensor components ? e.g R_φθφθ . and ricci tensor components.

dynamical system : 


@Preben Alsholm brilliant work ! appreciate what you have done .

@Preben Alsholm brilliant work ! appreciate what you have done .

@PatrickT thank you for your help.

@PatrickT thank you for your help.

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